Question

If a member is subjected to tensile stress of ${}^{\prime }{p}_x^{\prime }$, compressive stress of ${}^{\prime }{p}_y^{\prime }$ and tensile stress of ${}^{\prime }{p}_z^{\prime }$, along the $X,Y$ and $Z$ directions respectively, then the resultant strain ${\epsilon }_x^{\prime }$; along the $X$ direction would be (E is Young's modulus of elasticity and 'μ' is Poisson's ratio)

• A. $\frac{1}{E}(p_x+\mu p_y-\mu p_z)$
• B. $\frac{1}{E}(p_x+\mu p_y+\mu p_z)$
• C. $\frac{1}{E}(p_x-\mu p_y+\mu p_z)$
• D. $\frac{1}{E}(p_x-\mu p_y-\mu p_z)$

Answer 1

The correct option is A $\frac{1}{E}(p_x+\mu p_y-\mu p_z)$



${\epsilon }_x=\frac{p_x}{E}-\mu -\mu (-\frac{p_y}{E})-\mu \left(\frac{p_z}{E}\right)$
$\frac{1}{E}(p_x+\mu p_y-\mu p_z)$